This paper introduces a computational approach to support concept selection in multi-objective design. It is motivated by: (1) a common need to delay some decisions during conceptual design due to the presence of uncertainties; and (2) intentional delay of decisions for the purpose of maintaining several optional concepts, as suggested by the concurrent engineering procedure of Toyota. Here, for the first time, a multi-objective set-based concept (SBC) selection problem with delayed decisions is formulated and solved. SBCs are conceptual solutions, which are represented by sets of particular solutions, with each concept having a one-to-many relation with the objective space. Several novel notions, such as higher-level concepts, multi-model concepts and robust concepts to delayed decisions, are defined and used. These lead to an auxiliary multi-objective decision problem. The auxiliary objectives are concept optimality and variability, both paramount to concept selection, with concept variability strongly supporting the idea of intentionally keeping several useful alternatives as long as possible. Academic and engineering examples are provided to demonstrate the proposed approach and its applicability to real-life problems. The results demonstrate that the suggested technique may well support the process of delayed decision either when needed or when deliberately done.